Newton´s iteration for weighted least-square design of FIR filters

The solution of a weighted least-square (WLS) design problem of an finite impulse response (FIR) filter can be found by solving a linear system of equations. So, most of the design computation are related to the evaluation of the inverse of a matrix, since is a related problem. In this paper, a new iterative procedure is developed for the inversion of the matrices involved in the design. By expanding the computation of the inverse of a matrix using Newton´s iteration, an updating formula for evaluating the inverse at each iteration is obtained. It is also shown that the proposed iterative procedure is applicable for arbitrary desired frequency responses. In addition, linear constraints on the coefficients can be easily included.